It is given that if the sequence is geometric, then its ratio of consecutive terms is constant. It is also given that the ratio of consecutive terms of the sequence is not constant. Which of the following must be true?

Answer and explanation

Correct answer: C. The sequence is not geometric

  1. Step 1: Let : 'the sequence is geometric' and : 'the ratio is constant'. We are told and .
  2. Step 2: If were true, would follow, contradicting . So (modus tollens).
Answer
The sequence is not geometric.
Why not the others: The other options either assert (which leads to a contradiction) or assert (which contradicts the second fact); 'geometric or constant ratio' is false because both parts are false.

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